The structure of free prosupersolvable groups (Q791640)

The author studies Sylow p-subgroups in supersolvable and prosupersolvable \(\Pi\)-groups, \(\Pi\) being a set of primes. Using a construction of such a group based on semidirect products of free pro-p- groups he manages to obtain best possible bounds for the number of generators of a p-subgroup of a finitely generated prosupersolvable \(\Pi\)-group. Another corollary of this construction is the freeness of p- Sylow subgroups of a free prosupersolvable \(\Pi\)-group (in the sense of pro-p-groups). There are also some other results on Sylow systems and automorphisms of the groups in the title. Previous approaches to these groups were via topology or cohomology [\textit{B. Oltikar}, On prosupersolvable groups and subgroups of free pro-C-products of pro-C- groups, Thesis, Carleton Univ. (1977) and \textit{B. Oltikar} and \textit{L. Ribes}, Pac. J. Math. 77, 183-188 (1978; Zbl 0406.20027)].